Methods of elimination in quota preferential STV

[David Catchpole]

On Fri, 6 Oct 2000, LAYTON Craig wrote:

> While it is unarguably crucial to discuss the ideal single winner method
> (both simply in terms of the logic of majoritarian decision making on
> specific issues and in cases eg presidential elections, where only one
> winner is possible), are you all sure that you should be advocating any of
> these systems for the election of a legislature?
> 
> Perhaps in terms of political expediency, yes (but some aren't so concerned
> with political expediency).
> 
> It doesn't seem that the accuracy of single winner systems have any
> relevance at all in a multi-member decision making body.  The overall result
> is always fairly random, and depends more on electoral boundaries than
> anything else.  All reasonably good multi member systems (like Bart's below,
> or David's, or Demorep's variable voting power, or standard quota
> preferential STV) will always produce a more accurate result than single
> winner, no matter how carefully derived the single winner system.

Woohoo! Someone who agrees with _me_!

This list's undue focus on single-winner methods has a lot to do with
their apparent ease of analysis. But I'm hoping useful work can be done on
the less depressing multi-winner methods.

> 
> CVD gets alot of flack, but they do advocate PR wherever possible (and only
> IRV where it seems that PR is too much of an uphill battle).
> 
> There is, I know, long standing prejudice against multi winner systems, and
> there's always Federalism to contend with.  But, even in relation to the
> latter, it's important to note that even wildly differing electorate sizes
> will still produce better results than single winner systems (ie, make each
> state an electorate with either 5, 7 or 9 members, depending on the state's
> size.  The fact that some states are ten times larger than others won't
> affect the result as much as single winner electorates, and will keep the
> smaller states happy).  Of course, it has to be unicameral, which is another
> change that is perhaps too radical to suggest.  Nevertheless, if you're
> after the best system.....
> 
> -----Original Message-----
> From: Bart Ingles [mailto:bartman at netgate.net]
> Sent: Thursday, 5 October 2000 15:20
> To: election-methods-list at eskimo.com
> Subject: Re: Methods of elimination in quota preferential STV
> 
> 
> I haven't had time to think about multi-winner methods much, but I have
> been leaning toward a modified cumulative voting method with
> elimination.  I'm pretty sure the following method has been shown to
> violate monotonicity & participation (see below), but I suspect the
> violations may be less severe than STV's. 
> 
> Voters simply vote for multiple candidates, as they would with approval
> voting, except that each choice gets an equal fraction of the vote (e.g.
> if you vote for five candidates, each gets 1/5 of your vote).  You then
> eliminate the weakest candidate and recount, so that the remaining
> candidates get a larger share (if one candidate was eliminated from your
> ballot, the remaining candidates now each get 1/4 of a vote).  Continue
> eliminating candidates in the same fashion until the required number
> remain.
> 
> No quotas are necessary since each voter always has the same cumulative
> vote.  The fact that voters must weigh compromise choices rather than
> simply rank them should yield higher overall utilities, and the method
> is certainly simpler than STV.
> 
> I have the following references regarding the method (I haven't seen
> them):
> 
> Bolger, E. M. (1983), "Proportional representation" in: S. J. Brams, W.
> F. Lucas and P. D. Straffin, Jr., eds., Modules in Applied Mathematics,
> Vol. 2 (Springer-Verlag, New York) 19-31.
> 
> Bolger, E. M. (1985), "Monotonicity and other paradoxes in some
> proportional representation schemes," SIAM Journal on Algebraic and
> Discrete Methods 6: 283-291.
> 
> -Bart
> 
> 

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